本文選題：混合不確定性 + 模糊收益率��； 參考：《大連理工大學(xué)》2013年碩士論文

【摘要】：經(jīng)典投資組合理論中,用收益率的方差衡量投資組合的風(fēng)險(xiǎn),其前提假設(shè)是收益率服從正態(tài)分布。這一前提與現(xiàn)實(shí)情況并不相符,證券收益的隨機(jī)不確定性和模糊不確定性同時(shí)存在。因此,論文引入混合熵作為衡量證券的風(fēng)險(xiǎn)的指標(biāo)。 混合熵可以表示由概率不確定性和模糊不確定性的混合不確定性。在不考慮模糊因素時(shí)且收益服從正態(tài)分布時(shí),混合熵與方差在衡量風(fēng)險(xiǎn)時(shí)等價(jià)；而在收益非正態(tài)分布以及考慮證券收益模糊性時(shí),由于證券的最高和最低收益的影響,混合熵在風(fēng)險(xiǎn)度量時(shí)相對(duì)方差法更加合理�；旌响馗倪M(jìn)了方差度量時(shí)僅考慮證券收益隨機(jī)性的缺陷,在證券風(fēng)險(xiǎn)衡量時(shí)更符合現(xiàn)實(shí)情況。 采用混合熵衡量投資組合的風(fēng)險(xiǎn)時(shí),由于不同證券之間的相關(guān)性時(shí)極其復(fù)雜,若忽略相關(guān)性建立線性規(guī)劃求解將導(dǎo)致所選擇的證券組合中證券數(shù)量?jī)H為1或2,有悖投資組合分散風(fēng)險(xiǎn)的初衷。因此,論文在忽略證券之間相關(guān)性建立線性規(guī)劃的同時(shí)加入了新的風(fēng)險(xiǎn)分散約束熵函數(shù),作為對(duì)忽略證券相關(guān)性以及投資組合證券數(shù)量過少的補(bǔ)償。利用matlab為計(jì)算工具,選取上證180指數(shù)中的十只證券進(jìn)行算例計(jì)算,同時(shí)變換風(fēng)險(xiǎn)分散約束熵函數(shù)在多目標(biāo)規(guī)劃問題中的權(quán)重求解最優(yōu)證券組合,可以明顯發(fā)現(xiàn),當(dāng)風(fēng)險(xiǎn)分散約束熵函數(shù)的權(quán)重增加時(shí),最優(yōu)組合中的證券數(shù)量明顯增加,組合的總風(fēng)險(xiǎn)相對(duì)穩(wěn)定。
[Abstract]:In classical portfolio theory, the risk of portfolio is measured by the variance of return rate, and the premise is that the yield is assumed to be normal distribution. This premise does not accord with the real situation, and the stochastic uncertainty and fuzzy uncertainty of the securities return exist simultaneously. Therefore, the mixed entropy is introduced to measure the risk of securities. Mixed entropy can represent the mixed uncertainty by probability uncertainty and fuzzy uncertainty. When the fuzzy factor is not considered and the return service is normal distribution, the mixed entropy and variance are equivalent in measuring the risk, while in the non-normal distribution of the income and the fuzziness of the income of the securities, because of the influence of the highest and the lowest return of the securities, The method of relative variance is more reasonable in risk measurement. The mixed entropy improves the variance measurement by considering only the randomness of security returns, which is more in line with the reality in the measurement of securities risk. When using mixed entropy to measure the risk of a portfolio, because the correlation between different securities is extremely complex, If the linear programming solution is established to ignore the correlation, the number of securities in the selected portfolio will be only 1 or 2, which is contrary to the original intention of portfolio diversification. Therefore, a new risk dispersion constraint entropy function is added to the linear programming to compensate for the neglect of the correlation between securities and the small number of portfolio securities. By using matlab as a calculation tool, ten securities in the 180 index of Shanghai Stock Exchange are selected for calculation. At the same time, the optimal portfolio can be found by transforming the weight of the entropy function of risk dispersion constraint in the multi-objective programming problem to solve the optimal portfolio. When the weight of the entropy function increases, the number of securities in the optimal portfolio increases obviously, and the total risk of the portfolio is relatively stable.
【學(xué)位授予單位】：大連理工大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2013
【分類號(hào)】：F830.59

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